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Paladinen [302]
3 years ago
10

Sue has to cut her grandma's grass this weekend and wants to know exactly how much area she will be cutting. Calculate the area

of the polygon. Be sure to show all your work and explain your answer.
Six-sided polygon that includes two isosceles right triangles, one with height and base of 25 feet, the other height and base of 8 feet, and one rectangle measuring 35 feet by 8 feet.

Mathematics
2 answers:
Roman55 [17]3 years ago
4 0
<span>Six-sided polygon that includes two isosceles right triangles, one with height and base of 25 feet,
triangle1 area= height * base /2
</span>triangle1 area= 25* 25/2= 312.5
<span>
the other height and base of 8 feet,
</span>triangle2 area= height * base /2
triangle2 area= 8* 8/2= 32
<span>
and one rectangle measuring 35 feet by 8 feet
</span>rectangle area= height * base 
rectangle area= 35* 8= 280

Total area= triangle1 area + triangle2 area + rectangle area= 312.5+ 32+280= 624.5
SCORPION-xisa [38]3 years ago
4 0

Hello,

The correct answer is 624.5

Hope this helps!!!! Happy Holidays!!!! (:

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Given that f(x) = √(ax + 1) , with x ≥ -1/a and a &gt; 0
padilas [110]

Answer:

\displaystyle 7

Step-by-step explanation:

first thing I assume by f~¹ you meant f^{-1} however

we want to find <u>a²</u><u>+</u><u>3</u><u>x</u><u>-</u><u>3</u><u> </u>for the given condition. with the composite function condition we can do so

<u>Finding</u><u> the</u><u> </u><u>inverse</u><u> of</u><u> </u><u>f(</u><u>x)</u><u>:</u>

\displaystyle f(x) =  \sqrt{ax + 1}

substitute y for f(x):

\displaystyle y=  \sqrt{ax + 1}

interchange:

\displaystyle x=  \sqrt{ay + 1}

square both sides:

\displaystyle  ay + 1  =  {x}^{2}

cancel 1 from both sides:

\displaystyle  ay =  {x}^{2}  - 1

divide both sides by a:

\displaystyle  y =   \frac{{x}^{2}  - 1 }{a}

substitute f^-1 for y:

\displaystyle   f ^{ - 1} (x) =   \frac{{x}^{2}  - 1 }{a}

<u>finding</u><u> the</u><u> </u><u>inverse</u><u> of</u><u> </u><u>g(</u><u>x)</u><u>:</u>

\displaystyle g(x) =   \frac{x + 1}{x}

substitute y for g(x)

\displaystyle y=   \frac{x + 1}{x}

interchange:

\displaystyle  \frac{y + 1}{y}  =x

cross multiplication

\displaystyle  y + 1= xy

cancel 1 from both sides

\displaystyle  y  - xy= - 1

factor out y:

\displaystyle  y(1  - x)= - 1

divide both sides by 1-x:

\displaystyle  y=    -  \frac{1}{ 1 - x}

substitute g^-1 for y:

\displaystyle  g ^{ - 1} (x)=    -  \frac{1}{ 1 - x}

remember that

\displaystyle (f   \circ g)x = f(g(x))

therefore we obtain:

\rm \displaystyle   (f ^{ - 1} \circ g ^{ - 1} ) (3) =   \frac{{  \bigg(- \dfrac{1}{1 - 3} }  \bigg)^{2}  - 1 }{a}

since (f~¹•g~¹)(3)=-⅜ thus substitute:

\rm \displaystyle    \frac{{  \bigg(- \dfrac{1}{1 - 3} }  \bigg)^{2}  - 1 }{a} =   - \frac{3}{8}

simplify parentheses:

\rm \displaystyle    \frac{{  \bigg( \dfrac{1}{2} }  \bigg)^{2}  - 1 }{a} =   - \frac{3}{8}

simplify square:

\rm \displaystyle    \frac{{   \dfrac{1}{4} }  - 1 }{a} =   - \frac{3}{8}

simplify substraction:

\rm \displaystyle     \frac{ - \dfrac{3}{4} }{ a}=   - \frac{3}{8}

simplify complex fraction:

\rm \displaystyle     - \dfrac{3}{4a} =   - \frac{3}{8}

get rid of - sign:

\rm \displaystyle      \dfrac{3}{4a} =    \frac{3}{8}

divide both sides by 3:

\rm \displaystyle      \dfrac{1}{4a} =    \frac{1}{8}

cross multiplication:

\rm \displaystyle      4a=    8

divide both sides by 4:

\rm \displaystyle      \boxed{ a=    2}

as we want to find <u>a²</u><u>+</u><u>3</u><u>a</u><u>-</u><u>3</u><u> </u>substitute the got value of a:

\displaystyle  {2}^{2}  + 3.2 - 3

simplify square:

\displaystyle 4  + 3.2 - 3

simplify multiplication:

\displaystyle 4  +6 - 3

simplify addition:

\displaystyle 10 - 3

simplify substraction:

\displaystyle 7

and we are done!

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Which is the side length of a cube with a volume of 125 m3?
Romashka [77]
The formula for the volume of a cube is:

V = a^3

Plug in what we know:

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4 years ago
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Sergio [31]

Answer:

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Step-by-step explanation:

We must find the area of each shape and add together. The area of a triangle is 1/2 base times height. The smaller triangles area is 2 and the larger triangle's area is 6. The area of the square is 4... so when all added together, we have 12.

3 0
3 years ago
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